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Metric and Topological Spaces
First part of this course note presents a rapid overview of metric spaces to set the scene for the main topic of topological spaces.Further it covers metric spaces, Continuity and open sets for metric spaces, Closed sets for metric spaces, Topological spaces, Interior and closure, More on topological structures, Hausdorff spaces and Compactness.
Author(s): T. W. Korner
102 Pages 
This is a review of the fundamental concepts of general topology. This note contains below topics, Topological Spaces, Continuous Maps, Connectedness, Separation Axioms, Compactness, A Taste of Topology in Functional Analysis.
Author(s): Farzad Shahi
288 Pages
Fans and their applications in General Topology Functional Analysis and Topological Algebra
This note contains below topics, Introduction and survey of main results, Some notation and general tools, Applications of strict Cldfans in General Topology, SFans Ssemifans and Dcofans in topological spaces, Strong Finfans in functions spaces, Strong Finfans in locally convex and Banach spaces with the weak topology, Topological functors and their properties, Constructing Finfans in topological algebras, Constructing fans in free universal algebras, Free objects in some varieties of topologized algebras.
Author(s): Taras Banakh
117 Pages
Lecture notes on generalized Heegaard splittings
This note contains below topics, Heegaard splittings, Generalized Heegaard splittings, Show Remark, Hence we have Claim, We give a proof of Proposition, By Lemma, Show the claim in the proof of Theorem, We prove Theorem, It follows from Lemma.
Author(s): Toshio Saito, Martin Scharlemann, Jennifer Schultens
66 Pages
This PDF covers the following topics related to Topology, Topology of Metric Spaces, Topological Spaces, Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces, and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito, Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces, Quotient Topology, Connected and Pathconnected Spaces, Compactness Revisited, Countability Axioms, Separation Axioms, Tychonoffs Theorem.
Author(s): IIT Kanpur
37 Pages
Topology I and II by Chris Wendl
This note describes the following topics, Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoffs theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampens theorem, Normal subgroups, generators and relations, The Seifertvan Kampen theorem and of surfaces, Torus knots, The lifting theorem, The universal cover and group actions, Manifolds, Surfaces and triangulations, Orientations and higher homotopy groups, Bordism groups and simplicial homology, Singular homology, Relative homology and long exact sequences, Homotopy invariance and excision, The homology of the spheres, Excision, The EilenbergSteenrod axioms, The MayerVietoris sequence, Mapping tori and the degree of maps, ocal mapping degree on manifolds Degrees, triangulations and coefficients, CWcomplexes, Invariance of cellular homology.
Author(s): Chris Wendl
382 Pages
General Topology by Tom Leinster
This note covers the following topics, Topological spaces, metric spaces, Topological properties, Subspaces, Compactness, Compact metric spaces, Connectedness, Connected subsets of the real line.
Author(s): Tom Leinster
85 Pages
String topology is the study of algebraic and differential topological properties of spaces of paths and loops in manifolds. Topics covered includes, Intersection theory in loop spaces, The cacti operad, String topology as field theory, A Morse theoretic viewpoint, Brane topology.
Author(s): Ralph L. Cohen and Alexander A. Voronov
95 Pages
Topology for the working mathematician
This note covers the following topics, Basic notions of pointset topology, Metric spaces, Completeness and its applications, Convergence and continuity, New spaces from old, Stronger separation axioms and their uses, Connectedness. Steps towards algebraic topology, Paths in topological and metric spaces, Homotopy.
Author(s): Michael Muger
407 Pages